The rotational and magnetic properties of many magnetic hot stars are poorly characterized, therefore the MiMeS and BinaMIcS collaborations have collected extensive high-dispersion spectropolarimetric datasets of these targets. We present longitudinal magnetic field measurements for 52 early B-type stars (B5 to B0), with which we attempt to determine their rotational periods Prot. Supplemented with high-resolution spectroscopy, low-resolution DAO circular spectropolarimetry, and archival Hipparcos photometry, we determined Prot for 10 stars, leaving only 5 stars for which Prot could not be determined. Rotational ephemerides for 14 stars were refined via comparison of new to historical magnetic measurements. The distribution of Prot is very similar to that observed for the cooler Ap/Bp stars. We also measured vsini and v_mac_ for all stars. Comparison to non-magnetic stars shows that vsini is much lower for magnetic stars, an expected consequence of magnetic braking. We also find evidence that v_mac_ is lower for magnetic stars. LSD profiles extracted using single-element masks revealed widespread, systematic discrepancies in between different elements: this effect is apparent only for chemically peculiar stars, suggesting it is a consequence of chemical spots. Sinusoidal fits to H line measurements (which should be minimally affected by chemical spots), yielded evidence of surface magnetic fields more complex than simple dipoles in 6 stars for which this has not previously been reported; however, in all 6 cases the second- and third-order amplitudes are small relative to the first-order (dipolar) amplitudes.